# 999 Cubed

999 cubed, 9993, is the number you get when multiplying 999 times 999 times 999. It can also be looked at as exponentiation involving the base 999 and the exponent 3. The term is usually pronounced 3rd power of nine hundred and ninety-nine or nine hundred and ninety-nine cubed. The cube of 999 is a perfect cube because the number is the product of the three equal integers 999. It can be written as 999 x 999 x 999 or in exponential form. Read on to learn everything about the number nine hundred and ninety-nine cubed, including useful identities.

9993 = 997002999
999 x 999 x 999 = 997002999

The inverse operation of cubing 999 is extracting the cube root of 999, explained here. In the next section we elaborate on the cube 999, and there you can also find our calculator.

## What is 999 Cubed

A cube is a three-dimensional shape with 6 equal square faces. Hence, a cube with side length 999 has an area of 997002999.

The sum and the differences of two cubes, for example with side length 999 and 998, can be calculated with the following formulas:

1. a3 + b3 = (a + b) × (a2 – ab + b2) ⇔ a3 = (a + b) × (a2 – ab + b2) – b3
With a = 999, b = 998 and the equivalence we get:
9993 = 1997 x (9992 – 999 × 998 + 9982) – 9983 = 1997 x (998001 – 997002 + 996004) – 994011992 = 1997 x 997003 – 994011992 = 997002999
2. a3 – b3 = (a – b) × (a2 + ab + b2) ⇔ a3 = (a – b) × (a2 + ab + b2) + b3
With a = 999, b = 998 and the equivalence we get:
9993 = (9992 + 999 × 998 + 9982) + 9983 = 998001 + 997002 + 996004 + 994011992 = 997002999

As follows from (1), 999 cubed can be calculated from 998 cubed and 999 squared using the identity:

n3 = (2 × n – 1) × (n2 -n + 1) – (n-1)3
9993 = (2 × 999 – 1) × (9992 – 999 + 1) – (998)3 = 1997 × (998001 – 998) – 994011992 = 1997 × 997003 – 994011992 = 997002999

Using the second formula 999 cubed can be also be computed with this identity:

n3 = (n-1)3 + 3n2 -3n + 1
9993 = 9983 + 3 × 9992 – 3 × 999 + 1 = 994011992 + 3 × 998001 – 3 × 999 + 1 = 994011992 + 2994003 – 2997 + 1 = 997002999

If you want to calculate the cube of any number, not only integers like 999, you can use our calculator below. Just enter your number; the calculation is then done automatically.

### Calculate Cubed Number

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You now know everything about the cube 999 and calculating it by means of multiplication, exponentiation, sum and difference formulas and using identities: 999 cubed is equivalent to 997002999.

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Note that you can also find many perfect cubes including 999 cubed using the search form in the sidebar of this page.

To sum up,

999 cubed = 999x999x999 = 9993 = 999 to the 3rd power = 997002999. The exponentiation form is mostly used to denote 999 cube.